It could also be due to a past event that Naruto unknowingly was involved in. Maybe something bad happened to Sarutobi's family or friends and he blames Naruto for it, whether it was Naruto's fault or not. For instance, if there was an attack on the village and Sarutobi lost someone close, and he wrongly believes Naruto had a part to play in it, he would start to hate Naruto.
It could be that Naruto has a different view of leadership than Sarutobi. Naruto might see Sarutobi's leadership as being too passive or too focused on maintaining the status quo. He, with his more energetic and revolutionary ideas, may resent Sarutobi for not being more progressive in making the village a better place for everyone, including himself.
Another reason might be related to a past event that Naruto unknowingly caused harm to one of the Team 7 members' families. Even if it was an accident, the emotional pain could make the affected member, and maybe the whole team, hold a grudge against Naruto. For instance, if Naruto's actions during a battle led to the destruction of a family's home, and a Team 7 member was from that family.
Naruto might initially be confused. He has always looked up to Sarutobi as a respected elder, so being hated by him would be unexpected. He would probably try to find out why Sarutobi hates him. For example, he might go to Sarutobi and ask directly, hoping for an explanation.
One possible reason could be a very different and perhaps unappealing take on Naruto's character in that fanfiction. Maybe the author made him overly cruel or out of character in ways that fans who love the original Naruto can't stand.
It could be that the fanfic portrays Hinata as being arrogant towards Naruto's past. Naruto has had a difficult childhood and if Hinata in the fanfic mocks or belittles that, it would make Naruto hate her. For instance, if she scoffs at his time as an outcast in the village and uses it as a means to elevate herself, Naruto would surely despise her for it.
One possible reason could be that he feels neglected. Maybe his family was always too busy with other things and didn't give him enough attention. This lack of attention during his formative years could have led to feelings of resentment.
One possible reason could be a misunderstanding. Maybe some false information was spread within the fanfic about the Uzumaki clan that made Naruto believe they were bad. For example, if there were lies about his family's past actions that he wrongly thought were true.
One possible reason could be a false accusation. Maybe someone spread a rumor that Naruto was involved in a heinous act, and without proper investigation, everyone turned against him.
One reason could be his power. His connection to the Nine - Tails makes him extremely powerful. In fanfiction, some in Konoha might fear this power and thus hate him. Another reason could be jealousy. Naruto becomes very popular and respected in the original story. But in fanfiction, some characters might be jealous of his achievements and turn that into hatred.
He could hate them because he felt they were absent during his difficult childhood. Naruto faced a lot of loneliness and bullying, and if he thought his parents could have prevented it but didn't, that would breed hatred.